More than a few chief executives in the streaming music space have said they expect a rising tide of users will lift all of their boats, and this week brought evidence suggesting they might be right. Spotify CEO Daniel Ek told an audience at an event sponsored by the Canadian telecommunications giant Rogers that since Apple Music launched less than three months ago, Spotify has been adding users and subscribers at a faster pace.

“We keep setting new records week by week,” Ek said at the event, according to a report in Bloomberg.

Ek declined to go into specifics about that growth, but it must be serious to surpass the trajectory Spotify has been on recently. After taking more than five years to reach 10 million paying subscribers around the world, it took Spotify just one year to get to 20 million -- the company announced it had reached that milestone in June. Ek pointed to partnerships with telcos like Rogers as a key driver in his speech in Toronto Monday.

In the run-up to Apple Music’s launch, the music and tech press spent plenty of time talking about how it would crush pure-play competitors like Spotify, which have struggled to achieve profitability even with billion-dollar revenues and millions of subscribers. That attention may have keyed Ek up a bit. He posted, then deleted, this tweet right after Apple unveiled Apple Music during its Worldwide Developers Conference earlier this summer:

danielek_ohok A tweet posted, then quickly deleted by Spotify CEO Daniel Ek. Photo: IBT

With so many prospective streaming customers unclaimed around the world, it’s far too early to label Apple Music a Spotify killer, but the service is off to a fine start. The company announced that it has 11 million active users around the world, and data from comScore indicated that Apple Music was one of the most widely used mobile apps in the United States in July, despite the fact that it is available on less than half of the country's smartphones.